基于递归相似性的非线性振动损伤敏感识别

Damage detection for non-linear vibration using recurrence similarity

对角线状分布是递归图和相干递归图最显著的视觉特征之一,其长度反映了系统动力学行为之间的相似性。基于最大对角线长,提出了评价两时间序列在重构相空间中演化趋势相似程度的定量指标,即最大相似度。将递归图方法引入到直杆的非线性纵振问题中,研究结果表明:针对不同损伤阶段,描述对角线长度的递归定量指标均能够有效识别出非线性结构的损伤,其中最大相似度指标对损伤最为敏感,特别适合于结构早期微小损伤的有效识别。

The diagonal line structure is one of the most important visual patterns in Recurrence Plots(RPs) and Cross Recurrence Plots(CRPs). Its length reflects the similar behavior between dynamic systems. Based on the longest diagonal length, a feature which can assess the degree of similarity between the dynamics of two different time series in the reconstructed phase space is presented. The RPs and CRPs technique is extended to the problemof non-linear elastic straight bar vibration systems, some damage features including the ones using diagonal lines structures have been extracted at each damage stage. The research results show that the Recurrence Quantification Analysis(RQA) features which measure the diagonal line length can effectively detect the damage of the nonlinear structure, and the similarity feature presented by using the longest diagonal length shows the greatest sensitivity to damage, it can be useful for the detection of small amounts of damage in structures.